High-Resolution Spectroscopy of $^{173}$Yb$^{+}$ Ions

Abstract

Compared to other stable isotopes of $\rm{Yb}^+$, $^{173}\rm{Yb}^+$ has a richer hyperfine structure, which leads to more favorable clock transitions, spectroscopic techniques for probing new physics, and more sophisticated quantum computing architectures. However, to date, its electronic spectrum remains poorly characterized. Here, we report on efficient laser cooling, state preparation, and detection of a single trapped $^{173}\rm{Yb}^+$ ion. The previously unobserved $^2\!S_{1/2} \rightarrow {}^2\!D_{3/2}$ electric quadrupole transition at 436 nm is coherently excited, and the isotope shift between $^{171}\rm{Yb}^+$ and $^{173}\rm{Yb}^+$ on this transition is determined with an uncertainty of 1.4 Hz. Using microwave spectroscopy, we resolve the hyperfine structure (HFS) of the ${}^2\!D_{3/2}$ state with a relative uncertainty below $10^{-8}$. From the HFS measurement data, we infer for ${}^{173}$Yb a nuclear magnetic octupole moment $Ω= -0.062(8)\,({\rm b} \times μ_N)$ with uncertainty reduced by more than 2 orders of magnitude compared to previous studies. The data also allow us to determine hyperfine anomalies for the ${}^2\!S_{1/2}$ and ${}^2\!D_{3/2}$ states.

Figures (3)

• Figure 1: Reduced energy level diagram of $^{173}$Yb$^+$ (not to scale). Laser cooling is realized on the $^2\!S_{1/2} \rightarrow {}^2\!P_{1/2}$ transition at 370 nm. Interruptions of the cooling cycle resulting from decay to the $^2\!D_{3/2}$ state are prevented using the repumping transition at 935 nm. Dotted lines indicate spontaneous decay, solid lines represent applied laser radiation, and dashed lines show additional spectral components of the laser radiation generated using electro-optic modulators. The component indicated by the long-dashed line is responsible for the depopulation of the $^2\!D_{3/2}(F=1)$ level and is thus deactivated during state detection.
• Figure 2: (a) Energy level diagram relevant for the $^2S_{1/2}(F=3) \rightarrow {}^2D_{3/2}(F=1)$ E2 transition with all Zeeman levels. (b) Spectra of $\pi$-pulse excitation on the E2 transitions from each Zeeman level of the $^2S_{1/2}(F=3)$ state. (c) Flow chart of the projective state preparation (PSP) using the E2 transition. Successful excitation of the 436 nm transition is indicated by the absence of fluorescence (dark) during detection. (d) Spectrum with $\pi$-pulse excitation and (e) observed Rabi flopping on the E2 transition between $m_F=0$ Zeeman levels using PSP. Deviations from full contrast are attributed to the ion temperature after Doppler cooling and the infidelity of the PSP process.
• Figure 3: The nuclear magnetic octupole moment $\Omega$ of $^{173}$Yb. The numbers beside the data points represent the corresponding values. Calculations (cal.) based on a single-particle model (Schwartz) Schwartz1955Xiao2020 and including nuclear deformation (Williams) Williams1962 are shown as triangles; experimental results (exp.) of Singh Singh2013 and Groote Groote2021 from HFS spectroscopy of the $^{3}\!P_2$ state in neutral $^{173}\rm{Yb}$ atoms are shown with results obtained in this work as circles.